R igraph manual pages

Centralize a graph according to the eigenvector centrality of vertices

Description

See centralize for a summary of graph centralization.

Usage

centr_eigen(
  graph,
  directed = FALSE,
  scale = TRUE,
  options = arpack_defaults,
  normalized = TRUE
)

Arguments

graph	The input graph.
directed	logical scalar, whether to use directed shortest paths for calculating eigenvector centrality.
scale	Whether to rescale the eigenvector centrality scores, such that the maximum score is one.
options	This is passed to eigen_centrality, the options for the ARPACK eigensolver.
normalized	Logical scalar. Whether to normalize the graph level centrality score by dividing by the theoretical maximum.

Value

A named list with the following components:

vector	The node-level centrality scores.
value	The corresponding eigenvalue.
options	ARPACK options, see the return value of eigen_centrality for details.
centralization	The graph level centrality index.
theoretical_max	The same as above, the theoretical maximum centralization score for a graph with the same number of vertices.

See Also

Other centralization related: centr_betw_tmax(), centr_betw(), centr_clo_tmax(), centr_clo(), centr_degree_tmax(), centr_degree(), centr_eigen_tmax(), centralize()

Examples

# A BA graph is quite centralized
g <- sample_pa(1000, m = 4)
centr_degree(g)$centralization
centr_clo(g, mode = "all")$centralization
centr_betw(g, directed = FALSE)$centralization
centr_eigen(g, directed = FALSE)$centralization

# The most centralized graph according to eigenvector centrality
g0 <- make_graph(c(2,1), n = 10, dir = FALSE)
g1 <- make_star(10, mode = "undirected")
centr_eigen(g0)$centralization
centr_eigen(g1)$centralization

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